With the blue filter producing a thin, vertical beam of light, Rosenstrauch placed the shard of glass in a clamp and adjusted the clamp on the long vertical rod so the light beam was exactly in the same orientation and struck the surface of the glass specimen at exactly right angles. "This will give us both a reference point and a way of calculating the correct angles later."

He then placed an eyepiece with a prism, lens and vernier scale on the rod behind the glass, and adjusted it until the thin blue beam of light registered directly on the zero value. He then let the two monks peer down the eyepiece and see for themselves how the light striking the glass passed directly though without being bent. This was not a trivial adjustment, or 'null' setting, and it would have taken someone less experienced much longer to get it right.

"Now for the refracted beam," he said, pleased with himself. Placing a mirror on a swivel some distance to the right of the lamp, Rosenstrauch first masked off most of the reflected light so it also became a thin vertical beam, which he then turned yellow with a different filter. By rotating the mirror the glass cutter was able to direct this yellow beam of light towards the glass shard so that it struck the surface at exactly the same spot as the blue light, but now at an acute angle.

As the two monks watched, he then slid the eyepiece sideways along the vernier scale until the yellow beam of light, emerging from the glass shard, was clearly visible as a soft, but distinct line in the center of the eyepiece. This adjustment, the positioning of the mirror, yellow light and the eyepiece took twice as long to establish as the 'normal' blue light had done, but eventually Brother Gregory and Brother Timothy were allowed to see the results.

"You see," Rosenstrauch said in triumph, "now all we have to do is take some measurements. Although I don't approve of the decadent French metric system we are forced to use, in this case the millimeter scale on those rulers will give us the most accurate results. Please check my readings as we go along."

Dutifully Mendel read, and reread the millimeter scales as Rosenstrauch measured four distances; the distance of the blue light from the glass, the distance of the mirror, and hence the yellow light, from the source of the blue light, and on the other side of the glass shard, the distance though the glass and the distance that the yellow light was displaced from the blue 'normal'.

After many tries and many corrections for possible errors, the three scientists had all the distances recorded, checked and re-checked.

"Now for the calculations. We begin by making use of trigonometry and right angle triangles," Rosenstrauch said, pushing some paper and a pen in Mendel's direction. "You do it," he said and explained how to use the measurements they had taken of the opposite and adjacent sides of the two triangles to calculate the hypotenuse.

This was not hard, as it was a simple use of the theorem of Pythagoras.

"All we have to do now is calculate the sine of the angle of incidence - the angle made by the two beams of light before they hit the first surface of the glass - and the sine of the angle of refraction - which is the angle between the two beams of light within the glass. That is the tricky part," he said, allowing Mendel to start the calculations while he looked over the monk's shoulder and pointed out errors.

Despite it's apparent complexity, the calculation was a simple one and soon accomplished. "Now, divide the two sines, and you have the refractive index of the glass," Rosenstrauch said, getting up to make some more tea. By the time he had got the water boiling again, Mendel was able to show him the results.

"Excellent," he exclaimed, putting down the pot, "you have got a value of 1.52, a value far too high for Waldglas and a genuine Krautstrunk Beaker."

"Could we do that all again?" Mendel asked, somewhat shocked by the results which seemed to add yet another layer of complication to his search for the real saboteur. So, somewhat reluctantly, the three of them chose another angle for the yellow and blue light and went through the tedious adjustments, measurements and finally the calculations. The results were unchanged - still 1.52 for the refractive index of the glass shard.

"This does not make sense," Mendel said in frustration as they sat and looked at the second set of calculations. "I hardly think that Oberstleutnant Reishach is lying. He said he got this beaker from his grandmother and that it is a family heirloom of some considerable age. How then can it be made of modern glass less than a decade old? Could we have made a mistake?"

"No," said Rosenstrauch carefully, "forensic science is still very new, but if I had to choose between believing this experiment and believing the words of a human, I would believe the numbers every time. I don't say that the Oberstleutnant is lying, but he is either wrong about the beaker, or trying to hide something.

"But what?" Brother Joseph asked, not for the first time in this investigation.

"A charitable view might be that Napp's nephew did indeed inherit a genuine beaker from his grandmother, but, for some reason later sold the real beaker for a high price. Fearing the wrath of his family he then went out and bought a fake and pretended it was the original, genuine one."

"I suppose that is the most reasonable explanation," said Lindenthal, taking the glass shard out of its clamp on the optical bench. "But I'm not sure it helps us at all. Does it really matter if the saboteur thought he was smashing a real beaker or a fake beaker?"

"Then there is the matter of the fire and the burning papers," Brother Gregory continued. "No matter how we try to explain the glass beaker, we also have to explain how anyone else but Brother Matthew could have started the fire."

Absently, for he was still trying to think of an answer, Brother Joseph removed the blue filter from before the powerful lamp, and took away the masking slit. The whole room was suddenly flooded in very bright light, which made them all blink. Then, without thinking, he bent down and was about to look through the eyepiece still on the optical bench.

Just as his head came parallel with the eyepiece the glass cutter gave him a violent push and shouted in alarm, "Don't look down that! You'll destroy your eyes!"

When everyone had settled down again, Herr Rosenstrauch explained. "The eyepiece consists of two converging lenses which bring the light to a focus right at the back of your eyeball. You were about to look at a powerful, naked light source and the concentration of the rays would have destroyed the back of your eye and made you go blind. Never do that!"

All of the men were shaken by Brother Joseph's narrow escape, so they calmed themselves down by drinking some more tea. When their nerves had stopped jumping, Mendel decided it was time to return to the monastery and report their latest findings to Abbot Napp. At the very least he could confront his nephew and see what he had to say about the fake beaker.